حل آخر :
let : f(x)=x/(1+x)in [a,b+c]wher a < b+c
note : f(x+y) and f(x) is increasing function by d f(x) /dx = 1/(1+x)^2 > 0 for all positive x
then f( a) < f(b+c) < f(b) + f(c) then
a/(1+a) وهو المطلوب Q.E.D